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Unsupervised Anomaly Localization using Variational Auto-Encoders
David Zimmerer, Fabian Isensee, Jens Petersen, Simon Kohl, Klaus Maier-Hein
TL;DR
Unsupervised VAE-based anomaly localization seeks to avoid architecture choices tailored to each evaluation problem. The paper complements reconstruction-based localization with a KL-divergence-derived term and reports stronger localization across many hyperparameter settings, with competitive maximum performance.
Problem
Reconstruction-based pixel-wise anomaly localization requires adapting the model architecture to the evaluated problem, conflicting with assumption-free unsupervised detection.
Method
The paper evaluates pixel-wise scores based on the reconstruction error, backpropagated ELBO and KL terms, and a combination of reconstruction error with KL-gradient information.
Results
The proposed approach outperforms reconstruction-error localization in most tested BraTS2017 hyperparameter settings, while the KL-term generally shows stronger sample-wise discrimination than reconstruction.
Takeaways & Limitations
The proposed approach is reported as robust to hyperparameter choice and transferable to new problems or datasets without modification.
Takeaways & Limitations
The pixel-wise gradient anomaly score relies on the assumption that the ELBO is locally convex.
Abstract
from arXiv · showhide
An assumption-free automatic check of medical images for potentially overseen anomalies would be a valuable assistance for a radiologist. Deep learning and especially Variational Auto-Encoders (VAEs) have shown great potential in the unsupervised learning of data distributions. In principle, this allows for such a check and even the localization of parts in the image that are most suspicious. Currently, however, the reconstruction-based localization by design requires adjusting the model architecture to the specific problem looked at during evaluation. This contradicts the principle of building assumption-free models. We propose complementing the localization part with a term derived from the Kullback-Leibler (KL)-divergence. For validation, we perform a series of experiments on FashionMNIST as well as on a medical task including >1000 healthy and >250 brain tumor patients. Results show that the proposed formalism outperforms the state of the art VAE-based localization of anomalies across many hyperparameter settings and also shows a competitive max performance.
1 Introduction
Unsupervised anomaly detection learns data distributions from unannotated subjects, offering a way to detect suspicious medical images without reference annotations. Deep-learning models, including VAEs, aim to avoid case-specific medical assumptions and annotated validation sets.
- Unsupervised models learn data distributions from large cohorts of unannotated subjects to detect out-of-distribution or diseased cases.
- Decoupling abnormality detection from reference annotations makes these approaches independent of human input and applicable across medical conditions and image modalities.
- Earlier unsupervised methods relied on explicit assumptions, such as manually designed image features, clustering, atlases, or natural anatomical symmetry.
- Deep learning addresses anomaly detection more systematically by learning normal data distributions rather than depending on case-specific medical knowledge or annotated validation sets.
2 Methods
The paper extends VAE-based anomaly localization beyond pixel-wise reconstruction error by using gradients of the ELBO and KL term, alongside a combined reconstruction–KL score. It evaluates these signals and their robustness across FashionMNIST and a healthy-to-tumor brain-imaging domain shift.
- VAE framework: VAEs optimize the evidence lower bound (ELBO) L to approximate data distributions, but architecture and data-dependent parameters can affect performance.Relevant choices include network architecture, latent-space size, decoder standard deviation c, and data dimension.
- Motivation: Pixel-wise reconstruction-error localization discards the KL term, although abnormality can arise from either component of the ELBO.This motivates incorporating information beyond reconstruction error for medical-image localization.
- Proposed localization methods: ELBO-grad uses the input derivative of L to produce a pixel-wise vector toward a sample with lower L, with gradient magnitude serving as the anomaly score under local convexity.The proposed interpretation relies on L being locally convex.
- Proposed localization methods: KL-grad and Rec-Grad differentiate the KL and reconstruction terms separately, while Combi multiplies KL-grad by reconstruction error to reduce noise artifacts and accommodate their different scales.Combi replaces the differentiated reconstruction term with direct reconstruction error.
- Experimental evaluation: Experiments compare ELBO, KL, and reconstruction signals and assess robustness across parameter settings using FashionMNIST and healthy HCP-to-tumor BraTS2017 data.FashionMNIST trains on 54,000 images from nine classes and tests on the unseen class; HCP includes 1,000 healthy patients and BraTS2017 includes 250 tumor patients, creating a domain shift.
3 Results
Across sample-wise and pixel-wise experiments, KL-based signals and the combined method generally outperform reconstruction error alone, while fine-tuned performance remains competitive with deep-learning anomaly-detection approaches.
- Sample-wise performance: The reconstruction term generally has lower sample-wise discriminative power than the KL-term or ELBO across tested parameter settings.Focusing only on reconstruction error can discard information contained in the KL-term.
- Pixel-wise performance: Figure 2 compares pixel-wise AUROC for reconstruction loss, KL-term gradient, reconstruction-term gradient, ELBO gradient, and the combi method.The comparison spans different VAE design choices on BraTS2017.
- Pixel-wise performance: Pixel-wise anomaly localization on BraTS2017 generally favors KL-Grad and the combi model over reconstruction error across hyperparameter settings.The model is trained on healthy HCP subjects and evaluated against whole-tumor annotations in BraTS2017.
- Hyperparameter tuning: AUROC values above 0.9 were achieved by the top-performing methods in the experiments.The KL-term showed robust performance across the tested settings, and the combi approach showed similar robustness.
- Hyperparameter tuning: Table 1 compares Dice scores for unsupervised whole-tumor detection on BraTS datasets across approaches.The caption states that the proposed approach is competitive with other deep-learning anomaly-detection methods but behind domain-knowledge-based non-deep-learning approaches.
- Hyperparameter tuning: Figure 3 visualizes five anomaly maps for each of six test samples: reconstruction error, KL-term, reconstruction-term, ELBO, and combi.The fine-tuned model is used for these sample visualizations.
4 Discussion & Conclusion
The proposed KL-complemented VAE localization approach is intended to preserve unsupervised anomaly detection while remaining robust across hyperparameters and transferable across problems or datasets.
- Discussion & Conclusion: The study compares VAE anomaly-detection approaches across many hyperparameter settings and finds that reconstruction error can often be improved by combining it with the backpropagated KL-term.The proposed combination reduces reliance on task-specific tuning while retaining competitive fine-tuned performance when annotated validation data are available.
- Discussion & Conclusion: The proposed approach is robust to the exact hyperparameter choice and could be transferred to new problems or datasets without modification.This supports preserving the unsupervised property without requiring manual optimization toward an annotated validation set.
- Discussion & Conclusion: The authors position the method as a step toward anomaly detection for medical imaging applications and potential radiological support tools using raw data.The stated motivation is to address the annotation data bottleneck.
ISLES 15
The supplied passages identify a 2D visualization section containing ELBO, KL-term, reconstruction-term, and gradient-magnitude displays, but do not state comparative findings.
- 2D Example & Visualizations: The 2D example section includes heatmaps for the ELBO, KL-term, and reconstruction term.These displays present visualizations of the component quantities used in anomaly analysis.
- 2D Example & Visualizations: The section also includes gradient visualizations for the ELBO, KL-term, and reconstruction term.The listed visualizations distinguish gradients of the separate terms.
- 2D Example & Visualizations: Gradient norms and gradient magnitudes are reported for the ELBO, KL-term, and reconstruction-term gradients.The passages do not provide a numerical comparison or stated outcome for these displays.